Problem: Solve for $x$ : $2\sqrt{x} + 6 = 9\sqrt{x} + 2$
Answer: Subtract $2\sqrt{x}$ from both sides: $(2\sqrt{x} + 6) - 2\sqrt{x} = (9\sqrt{x} + 2) - 2\sqrt{x}$ $6 = 7\sqrt{x} + 2$ Subtract $2$ from both sides: $6 - 2 = (7\sqrt{x} + 2) - 2$ $4 = 7\sqrt{x}$ Divide both sides by $7$ $\frac{4}{7} = \frac{7\sqrt{x}}{7}$ Simplify. $\dfrac{4}{7} = \sqrt{x}$ Square both sides. $\dfrac{4}{7} \cdot \dfrac{4}{7} = \sqrt{x} \cdot \sqrt{x}$ $x = \dfrac{16}{49}$